There are many classes of ill-posed problems that cannot be solved with existing iterative methods, since the usual Lipschitz-type assumptions are not satisfied. In this study, we expand the applicability of a two step Newton-type projection method considered in [10,11], using weaker assumptions. Numerical examples for the method and examples where the old assumptions are not satisfied but the new assumptions are satisfied are provided at the end of this study.
"Expanding the applicability of a Two Step Newton-type projection method for ill-posed problems." Funct. Approx. Comment. Math. 51 (1) 141 - 166, September 2014. https://doi.org/10.7169/facm/2014.51.1.8